About
This is a summer school course for anyone requiring the knowledge of topology. This course, Introduction to Topology, mainly consists of three topics:
- General topology;
- Fundamental groups;
- Singular/Cellular homology groups: basic theory and computations.
Our main reference is Armstrong’s Basic Topology. 中文版
If you feel it difficult to read or want a simpler or more suitable one, I suggest you Morris’s book Topology without tears.
If you tend to study more algebraic aspects of topology, Massey’ book A basic course in algebraic topology or Hatcher’s book Algebraic Topology seem to be nice choices.
Eilenberg S, Steenrod NE. Axiomatic Approach to Homology Theory. Proc Natl Acad Sci U S A. 1945 Apr;31(4):117-20. doi: 10.1073/pnas.31.4.117.
The handwritten lecture notes will be continuously updated until the end of this course.
- Lecture 01: Topological Spaces
- Lecture 02-03: Topological Properties
- Lecture 04: Classification of Surfaces
- Lecture 05: Fundamental Groups I
- Lecture 06: Fundamental Groups II
- Lecture 07: Fundamental Groups III
- Lecture 08: Singular Homology Groups I
- Lecture 09: Singular Homology Groups II
- Lecture 10: Singular Homology Groups III
- Lecture 11: Cellular Homology Groups